$\dfrac{ u - 5v }{ -4 } = \dfrac{ 9u + 8w }{ -9 }$ Solve for $u$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ u - 5v }{ -{4} } = \dfrac{ 9u + 8w }{ -9 }$ $-{4} \cdot \dfrac{ u - 5v }{ -{4} } = -{4} \cdot \dfrac{ 9u + 8w }{ -9 }$ $u - 5v = -{4} \cdot \dfrac { 9u + 8w }{ -9 }$ Multiply both sides by the right denominator. $u - 5v = -4 \cdot \dfrac{ 9u + 8w }{ -{9} }$ $-{9} \cdot \left( u - 5v \right) = -{9} \cdot -4 \cdot \dfrac{ 9u + 8w }{ -{9} }$ $-{9} \cdot \left( u - 5v \right) = -4 \cdot \left( 9u + 8w \right)$ Distribute both sides $-{9} \cdot \left( u - 5v \right) = -{4} \cdot \left( 9u + 8w \right)$ $-{9}u + {45}v = -{36}u - {32}w$ Combine $u$ terms on the left. $-{9u} + 45v = -{36u} - 32w$ ${27u} + 45v = -32w$ Move the $v$ term to the right. $27u + {45v} = -32w$ $27u = -32w - {45v}$ Isolate $u$ by dividing both sides by its coefficient. ${27}u = -32w - 45v$ $u = \dfrac{ -32w - 45v }{ {27} }$